Question

Consider the cubic polynomial y=Ax^3 +6x^2 -Bx, where A and B are unknown constants. If possible determine the values of A and B so that the graph of y has a maximum value at x=-1 and an inflection point at 1.

Answer 1

dy/dx = 3A x^2 + 12 x - B

this is 0 at x = -1 and at x = 1
so it has factors of
(x+1)(x-1)
or it is
x^2 -1
well, there is no x term so no 12 x term so sorry I can not do it.

Answer 2

y' = 3Ax^2 + 12x - B
y'(-1) = 0 so
0 = 3A - 12 - B
3A = B + 12

y'' = 6Ax + 12
y''(1) = 0 so
0 = 6A + 12
A = -2

so, B = -18

y = -2x^3 + 6x^2 + 18x